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Simplifying 0.5x4 + 3x2 + 6 = 0 Reorder the terms: 6 + 3x2 + 0.5x4 = 0 Solving 6 + 3x2 + 0.5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 12 + 6x2 + x4 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 6x2 + -12 + x4 = 0 + -12 Reorder the terms: 12 + -12 + 6x2 + x4 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6x2 + x4 = 0 + -12 6x2 + x4 = 0 + -12 Combine like terms: 0 + -12 = -12 6x2 + x4 = -12 The x term is 6x2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x2 + 9 + x4 = -12 + 9 Reorder the terms: 9 + 6x2 + x4 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + 6x2 + x4 = -3 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = -3 Can't calculate square root of the right side. The solution to this equation could not be determined.
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